UNIT-3KNOWLEDGE REPRESENTATION                           1
Agents that reason logically(Logicalagents)•   A Knowledge based Agent•   The Wumpus world environment•   Representation, ...
Abilities KB agent• Agent must be able to:   • Represent states and actions,   • Incorporate new percepts   • Update inter...
Agents that Reason Logically• Logical agents have knowledge base, from  which they draw conclusions   • TELL: provide new ...
Sample: Wumpus World• Show original wumpus game   • goal is to shoot wumpus   • example of logical reasoning• Our version:...
A Wumpus Agent• Agent does not perceive its own location (unlike  sample game), but it can keep track of where it  has bee...
Wumpus Agent• Actuators:   • Forward, Turn Left, Turn Right   • Grab (gold)   • Shoot (shoots arrow forward until hits    ...
Wumpus Agent• Death  • Agent dies if it enters a pit or square with    wumpus• Goal: get gold and climb back out. Don’t di...
Some complex reasoning examples• Start in (1,1)   • Breeze in (1,2) and (2,1)   • Probably a pit in (2,2)• Smell in (1,1) ...
Another example solutionNo perception  1,2 and 2,1 OK   B in 2,1  2,2 or 3,1 P?Move to 2,1                      1,1 V  ...
Example solutionS and No S when in 2,1  1,3 or 1,2 has W1,2 OK  1,3 WNo B in 1,2  2,2 OK & 3,1 P                       ...
AI Models and Pr opositionalLogic   •The Role of a Model   •Represent The Environment   •Assimilate Knowledge   •Learning ...
Models• If we are going to create programs that  are intelligent, then we need to figure out  how to represent models• The...
The Role of a Model• Represent the environment• Provide a structure for the assimilation of  new knowledge                ...
Represent The Environment• Features in the environment must be  represented as features in the model• They should be able ...
Assimilate Knowledge• A model of the world allows an agent to  organize new information in the context of  what it already...
Learning• An AI agent may start ready programmed  with knowledge, or it may have to learn it  from experience• The model m...
Simulation• Simulate the real environment to test  potential actions.• The model needs to accept simulated  sensory input ...
Inference• Inference is the process of deriving a  conclusion based on what is known                                      ...
Representation, Reasoning and logic                                 20
Logic in general                   21
Ontological and Epistemological Assumptions•    ontological assumption :It is understood in connection to the    logic of ...
Types of logic                 23
The use of logic• A logic: formal language for representing information,  rules for drawing conclusions• Two kinds of logi...
Entailment •   One thing follows from another         KB |= α (knowledge base entails alpha) •   KB entails sentence α if ...
Propositional Logic• Represents facts as being either true or false   • Formally represented by a letter, e.g. P or Q.   •...
Logic consists of•   Logical constants: true, false•   Proposition symbols: P, Q, R, ...•   Logical connectives: & (or ^),...
Basic symbols• Expressions only evaluate to either “true” or “false.”•   P           “P is true”•   ¬P          “P is fals...
For example              29
Syntax rules for propositional logic• The constants true and false are propositions by  themselves.• A proposition symbol ...
AmbiguityThe grammar can be ambiguous, for example:   P & Q ∨ R.It is best to use parentheses to eliminate ambiguity.When ...
Limitations of Propositional Logic1. It is too weak, i.e., has very limited expressiveness:•   Each rule has to be represe...
Inferencerules            33
An Agent for the wumpus world – PropositionalLogic                                            34
Example of using logic in Wumpus World                             •   KB contains:                                 ¬S1,1 ...
KB also contains knowledge of environment• No stench  no wumpus nearby    R1 : ¬S1,1 ⇒ ¬W1,1 ∧ ¬W1, 2 ∧ ¬W2,1    R2 : ¬S ...
We can determine where wumpus is!• Method 1: Truth table  • At least 14 symbols currently: S1,1, S2,1, S1,2, S2,2,    W1,1...
We can determine where wumpus is!• Method 2: Inference   • Modus Ponens         R1 : ¬S1,1 ⇒ ¬W1,1 ∧ ¬W1, 2 ∧ ¬W2,1       ...
Inference continued...  • Modus Ponens and And-Elimination again:     R2 : ¬S 2,1 ⇒ ¬W1,1 ∧ ¬W2,1 ∧ ¬W2, 2 ∧ ¬W3,1     ¬W1...
Inference continued...  • Unit Resolution:                         W1,1 ∨ W1, 2 ∨ W2, 2 ∨ W1,3                         ¬W1...
Determining action based on knowledge      A1, 2 ∧ W1,3 ∧ Forward A ⇒ Shoot      A1, 2 ∧ P ,3 ∧ Forward A ⇒ ¬Forward      ...
Propositional logic seems inefficient• Rule: “Shoot if the wumpus is in front of you”   • 16 x 4 = 64 rules for the 4x4 gr...
First-order logic to the rescue• Uses variables to represent generalities• Can reduce rules significantly                 ...
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Introduction iii

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Introduction iii

  1. 1. UNIT-3KNOWLEDGE REPRESENTATION 1
  2. 2. Agents that reason logically(Logicalagents)• A Knowledge based Agent• The Wumpus world environment• Representation, Reasoning and Logic• Logics – An Introduction• Propositional Logic• An Agent for the wumpus world – Propositional Logic 2
  3. 3. Abilities KB agent• Agent must be able to: • Represent states and actions, • Incorporate new percepts • Update internal representation of the world • Deduce hidden properties of the world • Deduce appropriate actions 3
  4. 4. Agents that Reason Logically• Logical agents have knowledge base, from which they draw conclusions • TELL: provide new facts to agent • ASK: decide on appropriate action 4
  5. 5. Sample: Wumpus World• Show original wumpus game • goal is to shoot wumpus • example of logical reasoning• Our version: • Find gold, avoid wumpus, climb back out of cave 5
  6. 6. A Wumpus Agent• Agent does not perceive its own location (unlike sample game), but it can keep track of where it has been• Percepts: • Stench – wumpus is nearby • Breeze – pit is nearby • Glitter – gold is here • Bump – agent has just bumped against a wall • Scream – agent has heard another player die 6
  7. 7. Wumpus Agent• Actuators: • Forward, Turn Left, Turn Right • Grab (gold) • Shoot (shoots arrow forward until hits wumpus or wall) • agent only has one arrow • Climb (exit the cave)• Environment: • 4x4 grid, start at (1,1) facing right 7
  8. 8. Wumpus Agent• Death • Agent dies if it enters a pit or square with wumpus• Goal: get gold and climb back out. Don’t die. • 1000 points for climbing out of cave with gold • 1 point penalty for each action taken • 10,000 point penalty for death 8
  9. 9. Some complex reasoning examples• Start in (1,1) • Breeze in (1,2) and (2,1) • Probably a pit in (2,2)• Smell in (1,1) – where can you go? • Pick a direction – shoot • Walk in that direction • Know where wumpus is 9
  10. 10. Another example solutionNo perception  1,2 and 2,1 OK B in 2,1  2,2 or 3,1 P?Move to 2,1 1,1 V  no P in 1,1 Move to 1,2 (only option) 10
  11. 11. Example solutionS and No S when in 2,1  1,3 or 1,2 has W1,2 OK  1,3 WNo B in 1,2  2,2 OK & 3,1 P 11
  12. 12. AI Models and Pr opositionalLogic •The Role of a Model •Represent The Environment •Assimilate Knowledge •Learning •Simulation •Inference 12
  13. 13. Models• If we are going to create programs that are intelligent, then we need to figure out how to represent models• They allow us to predict certain things about the future. 13
  14. 14. The Role of a Model• Represent the environment• Provide a structure for the assimilation of new knowledge 14
  15. 15. Represent The Environment• Features in the environment must be represented as features in the model• They should be able to act in the model just as they do in the environment• Needs to be able to represent both long term qualities of the environment and short term states. 15
  16. 16. Assimilate Knowledge• A model of the world allows an agent to organize new information in the context of what it already knows and draw conclusions. 16
  17. 17. Learning• An AI agent may start ready programmed with knowledge, or it may have to learn it from experience• The model may change in response to new experiences. 17
  18. 18. Simulation• Simulate the real environment to test potential actions.• The model needs to accept simulated sensory input and it needs to feed simulated actions back in without actually making those actions in reality• It needs an imagination 18
  19. 19. Inference• Inference is the process of deriving a conclusion based on what is known 19
  20. 20. Representation, Reasoning and logic 20
  21. 21. Logic in general 21
  22. 22. Ontological and Epistemological Assumptions• ontological assumption :It is understood in connection to the logic of functioning of the agent. - question is: “What does the agent do?” This means discussing both what the agent is and what its behavior constitutes of.• Epistemological assumptions: It consider the nature of knowledge. - question is: “On what knowledge does the agent base its actions?” It is important to discuss the origins of knowledge as well as concepts such as learning and memory. 22
  23. 23. Types of logic 23
  24. 24. The use of logic• A logic: formal language for representing information, rules for drawing conclusions• Two kinds of logics:• Propositional Logic • Represents facts P∧Q ⇒ R • First Order Logic • Represents facts, objects, and relations ∀x Cat ( x) ⇒ Mammal ( x) 24
  25. 25. Entailment • One thing follows from another KB |= α (knowledge base entails alpha) • KB entails sentence α if and only if α is true in worlds where KB is true. Ε.g. x+y=4 entails 4=x+y • Entailment is a relationship between sentences that is based on semantics. 25
  26. 26. Propositional Logic• Represents facts as being either true or false • Formally represented by a letter, e.g. P or Q. • Actually refer to facts about the environment, e.g. the speed limit in town is 30mph• Single facts can be combined into sentences using Boolean operators• These sentences, if true, can become facts in the KB.• A KB is said to entail a sentence if it is true in the KB 26
  27. 27. Logic consists of• Logical constants: true, false• Proposition symbols: P, Q, R, ...• Logical connectives: & (or ^), ∨, ¬, →, ↔• Parentheses: ( )• Propositional logic is an extremely simple representation 27
  28. 28. Basic symbols• Expressions only evaluate to either “true” or “false.”• P “P is true”• ¬P “P is false” negation• PVQ “either P is true or Q is true or both” disjunction• P^Q “both P and Q are true” conjunction• P => Q “if P is true, the Q is true” implication• PQ “P and Q are either both true or both false” equivalence 28
  29. 29. For example 29
  30. 30. Syntax rules for propositional logic• The constants true and false are propositions by themselves.• A proposition symbol such as P or Q is a proposition by itself.• Wrapping parentheses around a proposition produces proposition. 30
  31. 31. AmbiguityThe grammar can be ambiguous, for example: P & Q ∨ R.It is best to use parentheses to eliminate ambiguity.When ambiguity is present, we resolve it with operator precedence: (highest) : ¬ ,& ,∨ ,⇒ , ⇔ (lowest) For example: ¬P ∨ Q & R )⇒ S is equivalent to: ((¬ P) ∨ (Q & R)) ⇒ S 31
  32. 32. Limitations of Propositional Logic1. It is too weak, i.e., has very limited expressiveness:• Each rule has to be represented for each situation: e.g., “don’t go forward if the wumpus is in front of you” takes 64 rules2. It cannot keep track of changes:• If one needs to track changes, e.g., where the agent has been before then we need a timed-version of each rule. To track 100 steps we’ll then need 6400 rules for the previous example. Its hard to write and maintain such a huge rule-base Inference becomes intractable 32
  33. 33. Inferencerules 33
  34. 34. An Agent for the wumpus world – PropositionalLogic 34
  35. 35. Example of using logic in Wumpus World • KB contains: ¬S1,1 ¬B1,1 ¬S 2,1 B2,1StenchAgent S1, 2 ¬B1, 2Start Breeze ¬S 2 , 2 ¬B2, 2 35
  36. 36. KB also contains knowledge of environment• No stench  no wumpus nearby R1 : ¬S1,1 ⇒ ¬W1,1 ∧ ¬W1, 2 ∧ ¬W2,1 R2 : ¬S 2,1 ⇒ ¬W1,1 ∧ ¬W2,1 ∧ ¬W2, 2 ∧ ¬W3,1 R3 : ¬S1, 2 ⇒ ¬W1,1 ∧ ¬W1, 2 ∧ ¬W2, 2 ∧ ¬W1,3• Stench  wumpus nearby R4 : S1, 2 ⇒ W1,1 ∨ W1, 2 ∨ W2, 2 ∨ W1,3 36
  37. 37. We can determine where wumpus is!• Method 1: Truth table • At least 14 symbols currently: S1,1, S2,1, S1,2, S2,2, W1,1, W2,1, W1,2, W2,2, W3,1, W1,3, B1,1, B2,1, B1,2, B2,2  214 rows, ouch! 37
  38. 38. We can determine where wumpus is!• Method 2: Inference • Modus Ponens R1 : ¬S1,1 ⇒ ¬W1,1 ∧ ¬W1, 2 ∧ ¬W2,1 ¬W1,1 ∧ ¬W1, 2 ∧ ¬W2,1 • And-Elimination ¬W1,1 ¬W1, 2 ¬W2,1 38
  39. 39. Inference continued... • Modus Ponens and And-Elimination again: R2 : ¬S 2,1 ⇒ ¬W1,1 ∧ ¬W2,1 ∧ ¬W2, 2 ∧ ¬W3,1 ¬W1,1 ¬W2,1 ¬W2, 2 ¬W3,1 • One more Modus Ponens: R4 : S1, 2 ⇒ W1,1 ∨ W1, 2 ∨ W2, 2 ∨ W1,3 W1,1 ∨ W1, 2 ∨ W2, 2 ∨ W1,3 39
  40. 40. Inference continued... • Unit Resolution: W1,1 ∨ W1, 2 ∨ W2, 2 ∨ W1,3 ¬W1,1 W1, 2 ∨ W2, 2 ∨ W1,3 ¬W2, 2 W1, 2 ∨ W1,3 ¬W1, 2 Wumpus is in (1,3)!!! W1,3 Shoot it. Shoot where? 40
  41. 41. Determining action based on knowledge A1, 2 ∧ W1,3 ∧ Forward A ⇒ Shoot A1, 2 ∧ P ,3 ∧ Forward A ⇒ ¬Forward 1• Propositional logic cannot answer well the question “What action should I take?”• It only answers “Should I take action X?” 41
  42. 42. Propositional logic seems inefficient• Rule: “Shoot if the wumpus is in front of you” • 16 x 4 = 64 rules for the 4x4 grid• Ditto for pits 42
  43. 43. First-order logic to the rescue• Uses variables to represent generalities• Can reduce rules significantly 43
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